A dispenser of this type is known from U.S. Pat. No. 3,361,305. The dispenser described therein has a pump chamber defined by a concave conical separation wall extending towards the interior of the container and an upwardly projecting conical membrane, with an outlet passage opening into said pump chamber at a position between said separation wall and said membrane and provided with the second check valve formed by a ball member and an associated valve seat. The separation wall is formed with a number of openings covered by a corresponding number of resilient flaps lying on said separation wall to form said first check valve by cooperation with the openings. After filling the container with the product to be dispensed, insertion of the closure piston in sealing engagement with the interior wall surface causes the product to flow through the openings of the first check valve into the pump chamber, so that the latter is substantially filled with the product in its expanded state. For dispensing the product, an exterior pressure is exerted on the membrane as with the thumb of a hand, causing the volume of the pump chamber to be reduced, whereby the product contained within the pump chamber is dispensed through the opened second check valve and the outlet passage. During this reduction of the pump chamber volume, the product cannot escape back towards the container, since the resilient flaps are firmly pressed down over the openings in the separating wall, so that the first check valve is closed. After the product has been displaced out of the pump chamber, the membrane is released, so that the volume of the pump chamber is again increased, whereby a suction force is produced to close the second check valve, preventing any outside air from entering the pump chamber through the outlet passage. The vacuum resulting from the increase of the pump chamber volume causes the first check valve to open by lifting the resilient flaps off the openings in the separation wall, so that the product may again flow from the container into the pump chamber to replenish the product supply therein. This known dispenser does not permit accurate metering of the product dispensed at a single stroke, since the membrane is returned to its original position only by virtue of its inherent resiliency, is subjected to fatigue effects and restricts the maximum volume of the pump chamber to a rather limited value.